Problem 5. Find the points on the surface xyz = 8 closest to the origin. Problem 6. Find the maximum volume of a rectangular box with surface area 600 cm2 and total edge length (the sum of all their sides) 120 cm. Problem 7. Find the smallest possible surface area of a rectangular box of volume 1 with one face a square. Problem 8. Let C be the intersection of the plane :13 + y + 22 = 1 and the ellipsoid 132 + y2 + % = 1. Use Lagrange multipliers to nd the points on C closest to the origin